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" The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference. "
Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ... - Página 18
por International Correspondence Schools - 1906
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - 1845 - 232 páginas
...proposition, a sin. A.~ c b sin. 68 FROPOSITION III. In any plane triangle, the sum of any two sides, is to their difference, as the tangent of half the sum of the angles opposite to them, is to the tangent of half their difference. Let ABC be any plane triangle,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 317 páginas
...difference as the radius to the tangent of the difference between either of them and 45°. PROP. IV. THEOR. The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference. Let ABC be any plane triangle...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 138 páginas
...triangle EFG, BC is drawn parallel to FG the base EC : CF : : EB : BG; that is, the sum of two sides is to their difference, as the tangent of half the sum of the angles at the base ia to the tangent of half their difference. * Moreover, the angles DBF, BFE are...
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A Treatise of Plane Trigonometry, and the Mensuration of Heights and ...

Jeremiah Day - 1848 - 153 páginas
...THE SUM OF THE OPPOSITE ANGLES ; TO THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half then- difference. Demonstration. Extend CA to G, making...
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Elements of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - 1848 - 324 páginas
...A + sin5 : sinlA — sin 7?, or (333) a + b : a—b : : tani(A+B) : tan^(^-S) ; ie PROPOSITION VI. The sum of any two sides of a triangle is to their dif- (396) ference, as the tangent of the half sum of the angles opposite to the tangent of half their...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - 1849 - 359 páginas
...+c 2 —a 2 ) = R« x -R- x " * Hence THEOREM V. In every rectilineal triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides, to the tangent of half their difference. * For. AB : BC : : sin C : sin...
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A Course of Mathematics: Containing the Principles of Plane Trigonometry ...

Jeremiah Day - 1851
...THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. Demonstration. Extend CA to G, making...
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ELEMENTS OF GEOMETRY AND TRIGONOMETRY

A. M. LEGENDRE - 1852
...AC :: sin 0 : sin jR THEOEEM II. In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 22. Let ACB be a triangle: then will AJ3...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - 1886 - 324 páginas
...C : sin B. Theorems. THEOREM 11. In any triangle, the sum of the two sides containing eithe1 angle, is to their difference, as the tangent of half the sum of (he t1eo other angles, to the tangent of half their di/ereMe. Let ACB be a triangle: then will With...
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A Course of Mathematics: Containing the Principles of Plane Trigonometry ...

Jeremiah Day - 1853 - 5 páginas
...of their opposite angles. It follows, therefore, from the preceding proposition, (Alg. 38'.>.) that the sum of any two sides of a. triangle, is to their difference ; as the tangent of half the sum of tin; opposite angles, to the tangent of half their difference. This is the second theorem npplied to...
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